Ron Harshbarger received his BS from Shippensburg State and an MST from the University of New Hampshire, did graduate work at Penn State University, and received a PhD from the University of Pittsburgh. During a long and highly successful career at Penn State University, Dr. Harshbarger received both teaching and advising awards. At Georgia Southern University, he taught a wide variety of undergraduate and graduate courses in mathematics, developed five new mathematics courses, and created the mathematics component for a new doctoral degree.

At the University of South Carolina Beaufort, Dr. Harshbarger was named Professor of the Year in 1999. In 2000, Professor Harshbarger was named the Governor’s Professor of the Year for the State of South Carolina. In 2001, the University of South Carolina Board of Trustees named him the Trustee Professor of the Year. In 2002, he received the Mathematical Association of America Southeastern Section Award for Distinguished University Teaching of Mathematics. He was nominated for the 2003 Haimo Award for Distinguished College or University Teaching of Mathematics, a national award given by the Mathematical Association of America. In 2003, he was also named Professor of the Year at the University of South Carolina Beaufort and given the Governor’s Distinguished Professor Award for the state of South Carolina.

Lisa Yocco received her undergraduate degree in mathematics from Augusta State University and her graduate degree in mathematics education from Florida State University. She has taught at both the college level and the high school level for twenty years, with her most recent experience at Georgia Southern University. She has co-authored several manuals in mathematics and graphing calculators and has presented workshops and papers at numerous conferences. In addition to her textbook writing and teaching, she enjoys spending time with her three children, cooking, and working on interior decorating.

Preface

To the Student

1. Functions, Graphs, and Models; Linear Functions

Algebra Toolbox

1-1 Functions and Models

1-2 Graphs of Functions

1-3 Linear Functions

1-4 Equations of Lines

Summary

Key Concepts and Formulas

Chapter 1 Skills Check

Chapter 1 Review

Group Activities/Extended Applications

2. Linear Models, Equations, and Inequalities

Algebra Toolbox

2-1 Algebraic and Graphical Solution of Linear Equations

2-2 Fitting Lines to Data Points: Modeling Linear Functions

2-3 Systems of Linear Equations in Two Variables

2-4 Solutions of Linear Inequalities

Summary

Key Concepts and Formulas

Chapter 2 Skills Check

Chapter 2 Review

Group Activities/Extended Applications

3. Quadratic, Piecewise-Defined, and Power Functions

Algebra Toolbox

3-1 Quadratic Functions; Parabolas

3-2 Solving Quadratic Equations

3-3 Piecewise-Defined Functions and Power Functions

3-4 Quadratic and Power Models

Summary

Key Concepts and Formulas

Chapter 3 Skills Check

Chapter 3 Review

Group Activities/Extended Applications

4. Additional Topics with Functions

Algebra Toolbox

4-1 Transformations of Graphs and Symmetry

4-2 Combining Functions; Composite Functions

4-3 One-to-One and Inverse Functions

4-4 Additional Equations and Inequalities

Summary

Key Concepts and Formulas

Chapter 4 Skills Check

Chapter 4 Review

Group Activities/Extended Applications

5. Exponential and Logarithmic Functions

Algebra Toolbox

5-1 Exponential Functions

5-2 Logarithmic Functions; Properties of Logarithms

5-3 Exponential and Logarithmic Equations

5-4 Exponential and Logarithmic Models

5-5 Exponential Functions and Investing

5-6 Annuities; Loan Repayment

5-7 Logistic and Gompertz Functions

Summary

Key Concepts and Formulas

Chapter 5 Skills Check

Chapter 5 Review

Group Activities/Extended Applications

6. Higher-Degree Polynomial and Rational Functions

Algebra Toolbox

6-1 Higher-Degree Polynomial Functions

6-2 Modeling with Cubic and Quartic Functions

6-3 Solution of Polynomial Equations

6-4 Polynomial Equations Continued; Fundamental Theorem of Algebra

6-5 Rational Functions and Rational Equations

6-6 Polynomial and Rational Inequalities

Summary

Key Concepts and Formulas

Chapter 6 Skills Check

Chapter 6 Review

Group Activities/Extended Applications

7. Systems of Equations and Matrices

Algebra Toolbox

7-1 Systems of Linear Equations in Three Variables

7-2 Matrix Solution of Systems of Linear Equations

7-3 Matrix Operations

7-4 Inverse Matrices; Matrix Equations

7-5 Determinants and Cramer’s Rule

7-6 Systems of Nonlinear Equations

Summary

Key Concepts and Formulas

Chapter 7 Skills Check

Chapter 7 Review

Group Activities/Extended Applications

8. Special Topics in Algebra

8-1 Systems of Inequalities

8-2 Linear Programming: Graphical Methods

8-3 Sequences and Discrete Functions

8-4 Series

8-5 Preparing for Calculus

8-6 The Binomial Theorem

8-7 Conic Sections: Circles and Parabolas

8-8 Conic Sections: Ellipses and Hyperbolas

Summary

Key Concepts and Formulas

Chapter 8 Skills Check

Chapter 8 Review

Group Activity/ Extended Applications

Appendices

A. Basic Graphing Calculator Guide

B. Basic Guide to Excel 2010 and Excel 2013

Photo Credits

Answers to Selected Exercises

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